Journal of the Korean Society for Precision Engineering (한국정밀공학회지)

Korean Society for Precision Engineering (한국정밀공학회)
권호 표지

A Learning Method of LQR Controller Using Jacobian

자코비안을 이용한 LQR 제어기 학습법

  • 임윤규 (울산산업진흥재단 전략기획단) ;
  • 정병묵 (영남대학교 공과대학 기계공학부)
  • Published : 2005.08.01
Download PDF
⟨ Previous Next ⟩

Abstract

Generally, it is not easy to get a suitable controller for multi variable systems. If the modeling equation of the system can be found, it is possible to get LQR control as an optimal solution. This paper suggests an LQR learning method to design LQR controller without the modeling equation. The proposed algorithm uses the same cost function with error and input energy as LQR is used, and the LQR controller is trained to reduce the function. In this training process, the Jacobian matrix that informs the converging direction of the controller Is used. Jacobian means the relationship of output variations for input variations and can be approximately found by the simple experiments. In the simulations of a hydrofoil catamaran with multi variables, it can be confirmed that the training of LQR controller is possible by using the approximate Jacobian matrix instead of the modeling equation and this controller is not worse than the traditional LQR controller.

Keywords

References

  1. Maciejowski, J. M., 'Multivariable feedback design,' Addison-Wesley Inc., 1989
  2. Franklin, G. F., Powell, J. D. and Emami-Naeini, A., 'Feedback Control of Dynamic Systems,' Addison-Wesley Inc., 2002
  3. Dorf, R. C. and Bishop, R. H., 'Modern Control Systems,' Addison-Wesley Inc., 1995
  4. Zhang, Y.M. and Kovacevic, R., 'Neurofuzzy model-based predictive control of weld fusion zone geometry,' IEEE Trans. on Fuzzy Systems, Vol. 6, No.3, pp. 389-401,1998 https://doi.org/10.1109/91.705507
  5. K. S. Narendra and K. Parthasarthy, 'Identification and control of dynamical system using neural network,' IEEE Trans. Neural Networks, Vol. 1, No. 1, pp. 4-27, 1990 https://doi.org/10.1109/72.80202
  6. Sanner, R. M. and Slotine, J. E., 'Gaussian networks for direct adaptive control,' IEEE Trans. Neural Networks, Vol. 3, pp. 837-863, 1992 https://doi.org/10.1109/72.165588
  7. Chen, F. C., 'Back-propagation neural networks for nonlinear self-tuning adaptive control,' IEEE Control System Magazine(Special issue on Neural Networks for Control Systems), Vol. 10, pp. 44-48, 1990 https://doi.org/10.1109/37.55123
  8. Chen, F. C. and Khalil, H. K., 'Adaptive control of nonlinear systems using neural networks,' Int. J. of Control, Vol. 55, pp. 1299-1317, 1992 https://doi.org/10.1080/00207179208934286
  9. Chung, B. M., 'Control of nonlinear multivariable Systems using direct fuzzy learning method,' Int. J. of Intelligent & Fuzzy Systems, Vol. 5, pp. 297-310, 1998
  10. Lim, Y.K. and Chung, B.M., 'PID learning method using gradient approach for optimal control,' J. of the KSPE, Vol. 18, No.1, pp. 180-186, 2001
  11. Lim, Y.K., Chung, B.M. and Cho, C.S., 'Optimal neural network controller design using Jacobian,' J. of the KSPE, Vol. 20, No.2, pp.85-93, 2002
  12. Lim, Y.K. and Chung, B.M., 'A learning method of PID controller by Jacobian in multi variable system,' J. of the KSPE, Vol. 20, No.2, pp.112-119, 2003
  13. Lee, S.Y., 'Theoretical and experimental study on the attitude control system of foil-catamaran,' Ph. D. thesis, Seoul National University, Korea, 1999